We present an approach for evolutionary design of the driving style of an agent, remotely operating a scale model of a car running in a fastest possible way. The agent perceives the environment from a video camera and conveys its actions to the car via standard radio control transmitter. In order to cope with the video feed latency we propose an anticipatory modeling in which the agent considers its current actions based on the anticipated intrinsic (rather than currently available, outdated) state of the car and its surrounding. The driving style is first evolved offline on a software model of the car and then adapted online to the real world. An online evolutionary adaptation of the offline-obtained best styles to the needs to avoid a small obstacle results in lap times that are virtually the same as the best lap times achieved on the same track without obstacles. Presented work is a step towards the automated design of the control software of remotely operated vehicles capable to find an optimal solution to various tasks in different environmental situations. The results, also, can be seen as an attempt to explore the feasibility of developing a framework of adaptive racing games in which the human competes against a computer with matching capabilities, both operating physical, scale models of cars.